Abstract

In this paper we consider the motion planning problem for closed chain systems.
We propose an extension of the PRM methodology which uses the
kinematics of the closed chain system to guide the generation and
connection of closure configurations.
In particular, we break the closed chains into a set of open subchains,
apply standard PRM random sampling techniques and forward kinematics
to one subset of the subchains, and then use inverse kinematics on the remaining
subchains to enforce the closure constraints. This strategy preserves
the PRM sampling philosophy, while addressing the fact that the
probability that a random configuration will satisfy the closure
constraints is zero, which has proven problematical in previous
attempts to apply the PRM methodology to closed chain systems.

Another distinguishing feature of our approach is that we adopt a
two-stage strategy, both of which employ the PRM framework.
First, we disregard the environment, fix the position and orientation
of one link (the ``virtual" base)
of the system, and construct a {\em kinematic roadmap} which
contains different self-collision-free closure configurations.
Next, we populate the environment with copies of the
kinematic roadmap (nodes and edges), and then use rigid body
planners to connect configurations of the same closure type.
This two-stage approach enables us to amortize the cost of computing
and connecting closure configurations.

Our results in 3-dimensional workspaces show that good roadmaps for
closed chains with many links can be constructed in a few seconds as
opposed to the several hours required by the previous purely
randomized approach.
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